The Southern Ocean Food Web
## Loading required package: knitrLoad required libraries:
require(igraph)
require(NetIndices)
require(reshape2)
require(ggplot2)
require(devtools)
require(vegan)Warning: there is no package called 'vegan'require(data.table)Source code for functions to describe web properties
url <- "https://raw.githubusercontent.com/jjborrelli/Ecological-Networks/master/FoodWebs/Rscripts/web_functions.R"
source_url(url)Load in the data
s.ocean <- read.csv("http://esapubs.org/archive/ecol/E092/097/diet.csv")
#s.ocean <- read.csv("~/Downloads/diet.csv")Whole Southern Ocean
el.df <- data.frame(pred = s.ocean$PREDATOR_NAME, prey = s.ocean$PREY_NAME)
SOgraph <- graph.edgelist(unique(as.matrix(el.df[,1:2])))
SOadjacency <- get.adjacency(SOgraph, sparse = F)First take a quick look at what the food web looks like. Here I plot the web by trophic level by setting the layout (code shown below). Nodes are plotted with trophic position along the y-axis and plotted along the x-axis according to a random uniform distribution (runif(x, 0, 1)).
par(mar = c(0,0,0,0))
layouts <- matrix(c(runif(gind$N), tind$TL), ncol = 2)
plot.igraph(SOgraph, layout = layouts, vertex.label = NA, edge.arrow.size = .5,
vertex.size = 1)
The plot of the web is not very helpful because there are so many species and far too many interactions. So looking at some of the whole web statistical properties and node properties may be more useful than just plotting the web.
The NetIndices and igraph packages have functions to calculate a number of commonly used food web indices. The function GenInd from the NetIndices library easily calculates the number of nodes (\(N\)), total number of links (\(L\)), link density (\(\frac{L}{N} = LD\)), and connectance (along with some other indices that are not relevant to this dataset). Connectance in this case is calculated as: \[C = \frac{L}{N*(N-1)}\]
The diameter is the single longest path between two nodes. The average.path.length is the mean number of links between any two nodes in the web. The clustering coefficient (or transitivity) is the probability that the nearest neighbors of a given vertex are themselves connected. A high clustering coefficient is an indication that a network has “small world” properties. The sum of the diagonal elements of the adjacency matrix gives the number of species that are cannibalistic, with links that loop back to themselves.
Species in a food web may be either basal, intermediate, or top. These positions may be determined simply by examining the degree of each node. The number of links pointing towards a node is its in-degree and the number of links pointing away from a node is the out-degree. In-degree is therefore a measure of how many species the node of interest preys upon (generality) while out-degree is the number of predators a given node has (vulnerability). Basal nodes will have an in-degree of 0, and likewise top species will have an out-degree of 0. Once the number of basal and top species are found, the number of intermediate species is simply the remainder.
gind <- GenInd(SOadjacency)
diam <- diameter(SOgraph)
avpath <- average.path.length(SOgraph)
cluster <- transitivity(SOgraph)
cannibals <- sum(diag(SOadjacency))
degrees <- degree(SOgraph, mode = "all")
indegrees <- degree(SOgraph, mode = "in")
outdegrees <- degree(SOgraph, mode = "out")
numBas <- length(indegrees[which(indegrees == 0)])
numTop <- length(outdegrees[which(outdegrees == 0)])
basal <- (numBas/gind$N) * 100
top <- (numTop/gind$N) * 100
int <- ((gind$N - (numBas + numTop))/gind$N) * 100
web.props <- data.frame(N = gind$N, L = gind$Ltot, LD = gind$LD, C = gind$C, D = diam,
AvgPath = avpath, ClCoef = cluster, Can = cannibals, Bas = basal, Top = top, Int = int) N L LD C D AvgPath ClCoef Can Bas Top Int
1 1095 10395 9.493 0.008677 6 2.114 0.1941 30 15.8 69.68 14.52There are a total of 1095 species with 10395 interactions among them. The longest chain described in this food web is 6 but the average chain is 2.1144.
The short average path length in the food web is made clearer by looking at the distribution of trophic positions in the Southern Ocean Food Web.
qplot(tind$TL, binwidth = .25, geom = "histogram",
xlab = "Trophic Position", ylab = "Frequency")
There is a tall bar at trophic level 1 and 2 representing plants and herbivores. There is a single organism, Chionodraco hamatus, with a trophic level between 1 and 2, suggesting that it consumes both plant and animals (a true omnivore). I am unconvinced, however, that the dataset includes a fully sampled food web and that some of those organisms described as basal are not plants, but are crustaceans, or other small organisms.
Most of the species in the food web are “top” predators with 70% of sampled species having no predators themselves. Plants (“basal species”) make up 16% of the web, and the remaining 15% are “intermediate”. The disproportionately large proportion of “top” species is unusual compared to other empirically described food webs and may be the result of sampling methods. The connectance of the Southern Ocean Food Web is relatively low at 0.0087, but that is expected with such a large number of species.
The degree distribution of a food web is often described as being power-law distributed, with most nodes having few links, and few nodes having many links. The degree distribution may be plotted as a histogram. Rather than fitting a power law to the distribution I have fit a lognormal distribution to the data, as it appears to be the better fit. In the following plot I have included a line fit to a lognormal (blue) and power law (green) distributions. The lognormal distribution appears to be a better fit to the degree distribution.
degdisfit <- fitdistr(degrees, "lognormal")
degdispow <- power.law.fit(degrees, force.continuous = T)
dd <- ggplot(data.frame(degrees = degrees), aes(x = degrees))
dd <- dd + geom_histogram(aes(y=..density..), binwidth = 5, colour = "black", fill = "white")
sequ <- seq(1, 300, .25)
dd <- dd + geom_line(aes(x = sequ[1:1095],
y = dlnorm(sequ[1:1095], degdisfit[[1]][1], degdisfit[[1]][2])),
colour = "blue")
dd <- dd + geom_line(aes(x = sequ[1:1095], y = 20 * sequ[1:1095] ^ -degdispow$alpha, colour = "green"))
dd + scale_y_continuous(limits = c(0, 0.12)) + theme(legend.position = "none")
motif_counter(list(SOgraph), webs = "Southern Ocean") web s1 s2 s3 s4 s5 d1 d2 d3 d4 d5 d6
1 Southern Ocean 66406 40066 0 301234 208502 2167 4193 1557 2470 1 129
d7 d8
1 30 13By location
The following code splits up the dataframe by the location column. The resulting 228 graph objects get stored in location.g. NOTE: the first location is a blank (" ") indicating that there are some rows without a location
places <- read.csv("C:/Users/jjborrelli/Desktop/GitHub/Ecological-Networks/SouthernOcean/locationLEVELS.csv")
placesC <- c()
for(i in 1:228){
placesC[i] <- as.character(places[[1]][i])
}
m <- split(s.ocean, f = s.ocean$LOCATION)
location.g <- list()
for (i in 1:length(levels(s.ocean$LOCATION))){
el.df <- data.frame(pred = m[[i]]$PREDATOR_NAME, prey = m[[i]]$PREY_NAME)
g <- graph.edgelist(unique(as.matrix(el.df[,1:2])))
location.g[[i]] <- g
}Plotting webs by location provides some idea about what trophic information was obtained from different sampling locations in the Southern Ocean.
par(mfrow = c(114, 2), mar = c(.01,.01,.01,.01))
for (i in 1:228){
plot.igraph(location.g[[i]], layout = layout.circle, edge.arrow.size = .5, vertex.label = NA,
vertex.size = 5)
text(0, 0, label = placesC[i], cex = 1.5)
}Warning: font width unknown for character 0x8f
Warning: font metrics unknown for character 0x8f
It is readily apparent from the food web plots that some sampling locations (e.g., Bay of Morbihan. Kerguelen Islands; Iles Crozets; Seal Island; etc.) included only a single predator with a portion of its prey. Others, like Amanda Bay and Rampen, included a single prey with some of its predators. A few locations, however, have enough species and interactions to be conisdered a near complete food web themselves (e.g., Croker Passage; Scotia Sea. Weddell Sea). Most webs have a small number of predators and prey and a few interactions. It is also worth noting that there appears to be several repeat locations in the data, such as Kerguelen Island, Kerguelen Island1, Kerguelen Islands, Kerguelen Islands1, Kerguelen waters. It may be best to merge webs with locations that are approximately the same. This might reduce the number of webs with only a handful of species.
Like the whole food web properties calculated above, indices can be calculated for each of the location subwebs.
web.props1 <- data.frame()
for (i in 1:228){
gind <- GenInd(get.adjacency(location.g[[i]], sparse = F))
diam <- diameter(location.g[[i]])
avpath <- average.path.length(location.g[[i]])
cluster <- transitivity(location.g[[i]])
cannibals <- sum(diag(get.adjacency(location.g[[i]], sparse = F)))
degrees <- degree(location.g[[i]], mode = "all")
indegrees <- degree(location.g[[i]], mode = "in")
outdegrees <- degree(location.g[[i]], mode = "out")
numBas <- length(indegrees[which(indegrees == 0)])
numTop <- length(outdegrees[which(outdegrees == 0)])
basal <- (numBas/gind$N) * 100
top <- (numTop/gind$N) * 100
int <- ((gind$N - (numBas + numTop))/gind$N) * 100
web.props <- data.frame(N = gind$N, L = gind$Ltot, LD = gind$LD, C = gind$C, D = diam,
AvgPath = avpath, ClCoef = cluster, Can = cannibals, Bas = basal,
Top = top, Int = int)
web.props1 <- rbind(web.props1, web.props)
}
print(web.props1) N L LD C D AvgPath ClCoef Can Bas Top Int
1 232 2158 9.3017 0.04027 4 1.261 0.020466 1 25.431 65.086 9.483
2 14 27 1.9286 0.14835 1 1.000 0.000000 0 28.571 71.429 0.000
3 16 15 0.9375 0.06250 1 1.000 0.000000 0 6.250 93.750 0.000
4 6 5 0.8333 0.16667 1 1.000 0.000000 0 16.667 83.333 0.000
5 14 13 0.9286 0.07143 1 1.000 0.000000 0 7.143 92.857 0.000
6 51 98 1.9216 0.03843 3 1.203 0.060484 2 29.412 62.745 7.843
7 5 4 0.8000 0.20000 1 1.000 0.000000 0 40.000 60.000 0.000
8 4 3 0.7500 0.25000 1 1.000 0.000000 0 25.000 75.000 0.000
9 32 33 1.0312 0.03327 2 1.057 0.000000 0 9.375 87.500 3.125
10 2 1 0.5000 0.50000 1 1.000 NaN 0 50.000 50.000 0.000
11 15 38 2.5333 0.18095 1 1.000 0.000000 0 33.333 66.667 0.000
12 3 2 0.6667 0.33333 1 1.000 0.000000 0 33.333 66.667 0.000
13 2 1 0.5000 0.50000 1 1.000 NaN 0 50.000 50.000 0.000
14 2 1 0.5000 0.50000 1 1.000 NaN 0 50.000 50.000 0.000
15 19 27 1.4211 0.07895 1 1.000 0.000000 0 10.526 89.474 0.000
16 43 42 0.9767 0.02326 1 1.000 0.000000 0 2.326 97.674 0.000
17 13 15 1.1538 0.09615 1 1.000 0.000000 0 23.077 76.923 0.000
18 4 3 0.7500 0.25000 1 1.000 0.000000 0 25.000 75.000 0.000
19 17 16 0.9412 0.05882 1 1.000 0.000000 0 5.882 94.118 0.000
20 3 2 0.6667 0.33333 1 1.000 0.000000 0 66.667 33.333 0.000
21 5 4 0.8000 0.20000 1 1.000 0.000000 0 20.000 80.000 0.000
22 167 337 2.0180 0.01216 2 1.259 0.003253 0 4.192 92.216 3.593
23 141 274 1.9433 0.01388 1 1.000 0.000000 0 8.511 91.489 0.000
24 2 1 0.5000 0.50000 1 1.000 NaN 0 50.000 50.000 0.000
25 39 38 0.9744 0.02564 1 1.000 0.000000 0 2.564 97.436 0.000
26 17 22 1.2941 0.08088 1 1.000 0.000000 0 23.529 76.471 0.000
27 6 5 0.8333 0.16667 1 1.000 0.000000 0 16.667 83.333 0.000
28 24 23 0.9583 0.04167 1 1.000 0.000000 0 4.167 95.833 0.000
29 23 43 1.8696 0.08498 1 1.000 0.000000 0 26.087 73.913 0.000
30 5 4 0.8000 0.20000 1 1.000 0.000000 0 20.000 80.000 0.000
31 61 60 0.9836 0.01639 1 1.000 0.000000 0 1.639 98.361 0.000
32 49 48 0.9796 0.02041 1 1.000 0.000000 0 2.041 97.959 0.000
33 3 2 0.6667 0.33333 1 1.000 0.000000 0 33.333 66.667 0.000
34 2 1 0.5000 0.50000 1 1.000 NaN 0 50.000 50.000 0.000
35 3 2 0.6667 0.33333 1 1.000 0.000000 0 33.333 66.667 0.000
36 2 1 0.5000 0.50000 1 1.000 NaN 0 50.000 50.000 0.000
37 23 22 0.9565 0.04348 1 1.000 0.000000 0 4.348 95.652 0.000
38 30 29 0.9667 0.03333 1 1.000 0.000000 0 3.333 96.667 0.000
39 16 15 0.9375 0.06250 1 1.000 0.000000 0 6.250 93.750 0.000
40 18 17 0.9444 0.05556 1 1.000 0.000000 0 5.556 94.444 0.000
41 4 3 0.7500 0.25000 1 1.000 0.000000 0 25.000 75.000 0.000
42 3 2 0.6667 0.33333 1 1.000 0.000000 0 33.333 66.667 0.000
43 2 1 0.5000 0.50000 1 1.000 NaN 0 50.000 50.000 0.000
44 27 36 1.3333 0.05128 1 1.000 0.000000 0 11.111 88.889 0.000
45 26 25 0.9615 0.03846 1 1.000 0.000000 0 3.846 96.154 0.000
46 10 9 0.9000 0.10000 1 1.000 0.000000 0 10.000 90.000 0.000
47 9 14 1.5556 0.19444 1 1.000 0.000000 0 22.222 77.778 0.000
48 24 23 0.9583 0.04167 1 1.000 0.000000 0 8.333 91.667 0.000
49 47 69 1.4681 0.03191 1 1.000 0.000000 0 6.383 93.617 0.000
50 25 24 0.9600 0.04000 1 1.000 0.000000 0 4.000 96.000 0.000
51 2 1 0.5000 0.50000 1 1.000 NaN 0 50.000 50.000 0.000
52 4 3 0.7500 0.25000 1 1.000 0.000000 0 25.000 75.000 0.000
53 113 2852 25.2389 0.22535 2 1.058 0.356413 10 69.912 21.239 8.850
54 32 50 1.5625 0.05040 1 1.000 0.000000 1 12.500 84.375 3.125
55 10 13 1.3000 0.14444 1 1.000 0.000000 0 30.000 70.000 0.000
56 31 30 0.9677 0.03226 1 1.000 0.000000 0 3.226 96.774 0.000
57 3 2 0.6667 0.33333 1 1.000 0.000000 0 33.333 66.667 0.000
58 113 225 1.9912 0.01778 2 1.277 0.006606 0 7.965 90.265 1.770
59 38 37 0.9737 0.02632 1 1.000 0.000000 0 2.632 97.368 0.000
60 27 52 1.9259 0.07407 2 1.136 0.025140 1 7.407 85.185 7.407
61 33 32 0.9697 0.03030 1 1.000 0.000000 0 3.030 96.970 0.000
62 10 9 0.9000 0.10000 1 1.000 0.000000 0 10.000 90.000 0.000
63 40 39 0.9750 0.02500 1 1.000 0.000000 0 2.500 97.500 0.000
64 17 16 0.9412 0.05882 1 1.000 0.000000 0 5.882 94.118 0.000
65 16 15 0.9375 0.06250 1 1.000 0.000000 0 6.250 93.750 0.000
66 10 9 0.9000 0.10000 1 1.000 0.000000 0 10.000 90.000 0.000
67 28 45 1.6071 0.05952 1 1.000 0.000000 0 25.000 75.000 0.000
68 41 40 0.9756 0.02439 1 1.000 0.000000 0 2.439 97.561 0.000
69 27 43 1.5926 0.06125 1 1.000 0.000000 0 29.630 70.370 0.000
70 24 33 1.3750 0.05978 2 1.158 0.101887 1 0.000 91.667 8.333
71 5 4 0.8000 0.20000 1 1.000 0.000000 0 20.000 80.000 0.000
72 5 4 0.8000 0.20000 1 1.000 0.000000 0 20.000 80.000 0.000
73 22 21 0.9545 0.04545 1 1.000 0.000000 0 4.545 95.455 0.000
74 4 3 0.7500 0.25000 1 1.000 0.000000 0 25.000 75.000 0.000
75 3 2 0.6667 0.33333 1 1.000 0.000000 0 33.333 66.667 0.000
76 3 2 0.6667 0.33333 1 1.000 0.000000 0 33.333 66.667 0.000
77 7 10 1.4286 0.23810 1 1.000 0.000000 0 28.571 71.429 0.000
78 2 1 0.5000 0.50000 1 1.000 NaN 0 50.000 50.000 0.000
79 22 23 1.0455 0.04978 1 1.000 0.000000 0 9.091 90.909 0.000
80 15 16 1.0667 0.07619 2 1.158 0.083333 0 6.667 86.667 6.667
81 84 151 1.7976 0.02166 1 1.000 0.000000 0 8.333 91.667 0.000
82 25 24 0.9600 0.04000 1 1.000 0.000000 0 4.000 96.000 0.000
83 12 12 1.0000 0.09091 1 1.000 0.000000 0 16.667 83.333 0.000
84 5 3 0.6000 0.15000 1 1.000 0.000000 0 60.000 40.000 0.000
85 7 11 1.5714 0.26190 1 1.000 0.000000 0 42.857 57.143 0.000
86 33 32 0.9697 0.03030 1 1.000 0.000000 0 3.030 96.970 0.000
87 16 15 0.9375 0.06250 1 1.000 0.000000 0 6.250 93.750 0.000
88 4 3 0.7500 0.25000 1 1.000 0.000000 0 25.000 75.000 0.000
89 8 7 0.8750 0.12500 1 1.000 0.000000 0 12.500 87.500 0.000
90 6 6 1.0000 0.20000 1 1.000 0.000000 0 33.333 66.667 0.000
91 72 77 1.0694 0.01506 1 1.000 0.000000 0 5.556 94.444 0.000
92 8 7 0.8750 0.12500 1 1.000 0.000000 0 12.500 87.500 0.000
93 22 21 0.9545 0.04545 1 1.000 0.000000 0 9.091 90.909 0.000
94 12 28 2.3333 0.21212 1 1.000 0.000000 0 58.333 41.667 0.000
95 13 12 0.9231 0.07692 1 1.000 0.000000 0 92.308 7.692 0.000
96 56 96 1.7143 0.03117 1 1.000 0.000000 0 5.357 94.643 0.000
97 67 115 1.7164 0.02601 1 1.000 0.000000 0 13.433 86.567 0.000
98 7 6 0.8571 0.14286 1 1.000 0.000000 0 14.286 85.714 0.000
99 4 3 0.7500 0.25000 1 1.000 0.000000 0 25.000 75.000 0.000
100 42 42 1.0000 0.02439 1 1.000 0.000000 0 4.762 95.238 0.000
101 31 54 1.7419 0.05806 2 1.054 0.034722 1 9.677 87.097 3.226
102 4 2 0.5000 0.16667 1 1.000 NaN 0 50.000 50.000 0.000
103 29 27 0.9310 0.03325 1 1.000 0.000000 0 10.345 89.655 0.000
104 5 4 0.8000 0.20000 1 1.000 0.000000 0 20.000 80.000 0.000
105 29 38 1.3103 0.04680 1 1.000 0.000000 0 10.345 89.655 0.000
106 50 165 3.3000 0.06735 2 1.125 0.306778 4 4.000 88.000 8.000
107 6 5 0.8333 0.16667 1 1.000 0.000000 0 16.667 83.333 0.000
108 9 8 0.8889 0.11111 1 1.000 0.000000 0 11.111 88.889 0.000
109 32 33 1.0312 0.03327 2 1.418 0.009119 1 0.000 93.750 6.250
110 48 67 1.3958 0.02970 1 1.000 0.000000 0 6.250 93.750 0.000
111 10 9 0.9000 0.10000 1 1.000 0.000000 0 10.000 90.000 0.000
112 35 37 1.0571 0.03109 1 1.000 0.000000 0 5.714 94.286 0.000
113 50 59 1.1800 0.02408 2 1.033 0.005515 1 8.000 88.000 4.000
114 23 42 1.8261 0.08300 1 1.000 0.000000 0 8.696 91.304 0.000
115 10 16 1.6000 0.17778 1 1.000 0.000000 0 20.000 80.000 0.000
116 35 34 0.9714 0.02857 1 1.000 0.000000 0 2.857 97.143 0.000
117 103 205 1.9903 0.01951 1 1.000 0.000000 0 10.680 89.320 0.000
118 10 9 0.9000 0.10000 1 1.000 0.000000 0 10.000 90.000 0.000
119 32 31 0.9688 0.03125 1 1.000 0.000000 0 3.125 96.875 0.000
120 13 12 0.9231 0.07692 1 1.000 0.000000 0 7.692 92.308 0.000
121 22 28 1.2727 0.06061 1 1.000 0.000000 0 13.636 86.364 0.000
122 3 2 0.6667 0.33333 1 1.000 0.000000 0 33.333 66.667 0.000
123 12 16 1.3333 0.12121 1 1.000 0.000000 0 75.000 25.000 0.000
124 52 51 0.9808 0.01923 1 1.000 0.000000 0 1.923 98.077 0.000
125 37 40 1.0811 0.03003 2 1.375 0.007874 0 5.405 91.892 2.703
126 25 46 1.8400 0.07667 1 1.000 0.000000 0 8.000 92.000 0.000
127 125 967 7.7360 0.06239 3 1.074 0.311741 4 36.800 56.000 7.200
128 30 29 0.9667 0.03333 1 1.000 0.000000 0 3.333 96.667 0.000
129 31 67 2.1613 0.07204 1 1.000 0.000000 0 25.806 74.194 0.000
130 13 12 0.9231 0.07692 1 1.000 0.000000 0 7.692 92.308 0.000
131 30 30 1.0000 0.03448 1 1.000 0.000000 1 0.000 96.667 3.333
132 5 4 0.8000 0.20000 1 1.000 0.000000 0 20.000 80.000 0.000
133 11 10 0.9091 0.09091 1 1.000 0.000000 0 9.091 90.909 0.000
134 30 29 0.9667 0.03333 1 1.000 0.000000 0 3.333 96.667 0.000
135 6 5 0.8333 0.16667 1 1.000 0.000000 0 16.667 83.333 0.000
136 19 27 1.4211 0.07895 1 1.000 0.000000 0 21.053 78.947 0.000
137 21 27 1.2857 0.06429 1 1.000 0.000000 0 19.048 80.952 0.000
138 7 6 0.8571 0.14286 1 1.000 0.000000 0 28.571 71.429 0.000
139 18 17 0.9444 0.05556 1 1.000 0.000000 0 5.556 94.444 0.000
140 29 49 1.6897 0.06034 1 1.000 0.000000 0 27.586 72.414 0.000
141 4 3 0.7500 0.25000 1 1.000 0.000000 0 50.000 50.000 0.000
142 6 8 1.3333 0.26667 1 1.000 0.000000 0 33.333 66.667 0.000
143 22 51 2.3182 0.11039 1 1.000 0.000000 0 31.818 68.182 0.000
144 2 1 0.5000 0.50000 1 1.000 NaN 0 50.000 50.000 0.000
145 3 2 0.6667 0.33333 1 1.000 0.000000 0 33.333 66.667 0.000
146 4 3 0.7500 0.25000 1 1.000 0.000000 0 25.000 75.000 0.000
147 22 22 1.0000 0.04762 1 1.000 0.000000 1 0.000 95.455 4.545
148 4 3 0.7500 0.25000 1 1.000 0.000000 0 25.000 75.000 0.000
149 27 26 0.9630 0.03704 1 1.000 0.000000 0 3.704 96.296 0.000
150 9 8 0.8889 0.11111 1 1.000 0.000000 0 11.111 88.889 0.000
151 8 7 0.8750 0.12500 1 1.000 0.000000 0 12.500 87.500 0.000
152 9 8 0.8889 0.11111 1 1.000 0.000000 0 22.222 77.778 0.000
153 4 3 0.7500 0.25000 1 1.000 0.000000 0 25.000 75.000 0.000
154 6 5 0.8333 0.16667 1 1.000 0.000000 0 16.667 83.333 0.000
155 8 12 1.5000 0.21429 1 1.000 0.000000 0 37.500 62.500 0.000
156 48 47 0.9792 0.02083 1 1.000 0.000000 0 2.083 97.917 0.000
157 32 31 0.9688 0.03125 1 1.000 0.000000 0 3.125 96.875 0.000
158 33 32 0.9697 0.03030 1 1.000 0.000000 0 3.030 96.970 0.000
159 30 29 0.9667 0.03333 1 1.000 0.000000 0 3.333 96.667 0.000
160 11 10 0.9091 0.09091 1 1.000 0.000000 0 9.091 90.909 0.000
161 22 21 0.9545 0.04545 2 1.764 0.000000 0 18.182 77.273 4.545
162 25 34 1.3600 0.05667 2 1.029 0.061644 0 24.000 72.000 4.000
163 2 1 0.5000 0.50000 1 1.000 NaN 0 50.000 50.000 0.000
164 30 29 0.9667 0.03333 1 1.000 0.000000 0 3.333 96.667 0.000
165 14 13 0.9286 0.07143 1 1.000 0.000000 0 7.143 92.857 0.000
166 14 13 0.9286 0.07143 1 1.000 0.000000 0 7.143 92.857 0.000
167 72 75 1.0417 0.01467 2 1.051 0.000000 1 5.556 91.667 2.778
168 56 62 1.1071 0.02013 1 1.000 0.000000 0 3.571 96.429 0.000
169 55 756 13.7455 0.25455 1 1.000 0.000000 0 50.909 49.091 0.000
170 24 52 2.1667 0.09420 1 1.000 0.000000 0 33.333 66.667 0.000
171 46 201 4.3696 0.09710 1 1.000 0.000000 0 19.565 80.435 0.000
172 41 378 9.2195 0.23049 1 1.000 0.000000 0 34.146 65.854 0.000
173 5 5 1.0000 0.25000 1 1.000 0.000000 0 40.000 60.000 0.000
174 7 6 0.8571 0.14286 1 1.000 0.000000 0 14.286 85.714 0.000
175 3 2 0.6667 0.33333 1 1.000 0.000000 0 33.333 66.667 0.000
176 2 1 0.5000 0.50000 1 1.000 NaN 0 50.000 50.000 0.000
177 58 65 1.1207 0.01966 2 1.030 0.013663 1 1.724 96.552 1.724
178 95 114 1.2000 0.01277 2 1.333 0.015446 2 0.000 97.895 2.105
179 16 20 1.2500 0.08333 1 1.000 0.000000 0 12.500 87.500 0.000
180 29 50 1.7241 0.06158 1 1.000 0.000000 0 31.034 68.966 0.000
181 34 73 2.1471 0.06506 1 1.000 0.000000 0 20.588 79.412 0.000
182 12 20 1.6667 0.15152 1 1.000 0.000000 0 16.667 83.333 0.000
183 8 9 1.1250 0.16071 1 1.000 0.000000 0 25.000 75.000 0.000
184 6 4 0.6667 0.13333 1 1.000 0.000000 0 33.333 66.667 0.000
185 160 527 3.2938 0.02072 2 1.165 0.069385 2 16.875 75.000 8.125
186 34 34 1.0000 0.03030 1 1.000 0.000000 1 0.000 97.059 2.941
187 46 67 1.4565 0.03237 1 1.000 0.000000 0 17.391 82.609 0.000
188 3 2 0.6667 0.33333 1 1.000 0.000000 0 33.333 66.667 0.000
189 10 12 1.2000 0.13333 1 1.000 0.000000 0 20.000 80.000 0.000
190 19 51 2.6842 0.14912 1 1.000 0.000000 0 73.684 26.316 0.000
191 15 14 0.9333 0.06667 1 1.000 0.000000 0 6.667 93.333 0.000
192 27 46 1.7037 0.06553 2 1.098 0.000000 0 22.222 74.074 3.704
193 24 35 1.4583 0.06341 1 1.000 0.000000 0 16.667 83.333 0.000
194 4 3 0.7500 0.25000 1 1.000 0.000000 0 25.000 75.000 0.000
195 3 2 0.6667 0.33333 1 1.000 0.000000 0 33.333 66.667 0.000
196 15 17 1.1333 0.08095 1 1.000 0.000000 0 46.667 53.333 0.000
197 63 84 1.3333 0.02151 1 1.000 0.000000 0 6.349 93.651 0.000
198 12 11 0.9167 0.08333 1 1.000 0.000000 0 8.333 91.667 0.000
199 41 40 0.9756 0.02439 1 1.000 0.000000 0 2.439 97.561 0.000
200 5 4 0.8000 0.20000 1 1.000 0.000000 0 20.000 80.000 0.000
201 4 3 0.7500 0.25000 1 1.000 0.000000 0 25.000 75.000 0.000
202 24 23 0.9583 0.04167 1 1.000 0.000000 0 4.167 95.833 0.000
203 2 1 0.5000 0.50000 1 1.000 NaN 0 50.000 50.000 0.000
204 23 22 0.9565 0.04348 1 1.000 0.000000 0 4.348 95.652 0.000
205 4 3 0.7500 0.25000 1 1.000 0.000000 0 25.000 75.000 0.000
206 2 1 0.5000 0.50000 1 1.000 NaN 0 50.000 50.000 0.000
207 14 13 0.9286 0.07143 1 1.000 0.000000 0 7.143 92.857 0.000
208 11 10 0.9091 0.09091 1 1.000 0.000000 0 9.091 90.909 0.000
209 23 21 0.9130 0.04150 1 1.000 0.000000 0 8.696 91.304 0.000
210 38 37 0.9737 0.02632 1 1.000 0.000000 0 2.632 97.368 0.000
211 8 7 0.8750 0.12500 1 1.000 0.000000 0 12.500 87.500 0.000
212 83 81 0.9759 0.01190 2 1.036 0.000000 0 2.410 96.386 1.205
213 7 6 0.8571 0.14286 1 1.000 0.000000 0 14.286 85.714 0.000
214 5 4 0.8000 0.20000 1 1.000 0.000000 0 40.000 60.000 0.000
215 27 34 1.2593 0.04843 1 1.000 0.000000 0 11.111 88.889 0.000
216 32 196 6.1250 0.19758 1 1.000 0.339161 3 12.500 78.125 9.375
217 8 7 0.8750 0.12500 1 1.000 0.000000 0 12.500 87.500 0.000
218 3 2 0.6667 0.33333 1 1.000 0.000000 0 33.333 66.667 0.000
219 22 21 0.9545 0.04545 1 1.000 0.000000 0 4.545 95.455 0.000
220 24 23 0.9583 0.04167 1 1.000 0.000000 0 4.167 95.833 0.000
221 33 32 0.9697 0.03030 1 1.000 0.000000 0 3.030 96.970 0.000
222 15 16 1.0667 0.07619 1 1.000 0.000000 0 26.667 73.333 0.000
223 11 10 0.9091 0.09091 1 1.000 0.000000 0 9.091 90.909 0.000
224 18 28 1.5556 0.09150 1 1.000 0.000000 0 27.778 72.222 0.000
225 18 25 1.3889 0.08170 1 1.000 0.000000 0 22.222 77.778 0.000
226 20 26 1.3000 0.06842 1 1.000 0.000000 0 30.000 70.000 0.000
227 12 18 1.5000 0.13636 1 1.000 0.000000 0 25.000 75.000 0.000
228 9 7 0.7778 0.09722 1 1.000 0.000000 0 22.222 77.778 0.000Because there are so many different locations (228) the dataframe of web properties becomes a bit unwieldy. Plotting the different indices is a useful way to examine some of the properties of the different locations’ food webs. First, a histogram of the number of nodes (N) in each web shows that most of the webs invovle less than 50 species, but a few are greater than 150 species.
ggplot(web.props1) + geom_histogram(aes(x = N), binwidth = 5)
A plot of connectance (C) against size (N) shows the expected relationship of a decline in connectance with size. It is also evident that most of the food webs in this study have a connectance less than 0.1. A number of webs have a connectance of 0.5, but those represent the locations with webs that are only two species with one interaction.
ggplot(web.props1) + geom_point(aes(x = N, y = C))
nn<- matrix(c(web.props1$Bas, web.props1$Int, web.props1$Top), nrow = 3, ncol = 228, byrow = T)
colnames(nn) <- as.character(1:228)
barplot(nn, col = c("blue", "yellow", "darkgreen"), xlab = "Web", ylab = "Percent")
By year
so.ode <- as.character(s.ocean$OBSERVATION_DATE_END)
so.ode.split <- strsplit(so.ode, split = "/")
year <- c()
for(i in 1:length(so.ode.split)){
year[i] <- so.ode.split[[i]][3]
}
s.ocean2 <- cbind(s.ocean, year)
m2 <- split(s.ocean2, f = s.ocean2$year)
year.g <- list()
for (i in 1:length(levels(s.ocean2$year))){
el.df <- data.frame(pred = m2[[i]]$PREDATOR_NAME, prey = m2[[i]]$PREY_NAME)
g <- graph.edgelist(unique(as.matrix(el.df[,1:2])))
year.g[[i]] <- g
}Plot webs by year
par(mfrow = c(23, 2), mar = c(.01,.01,.01,.01))
for (i in 1:45){
plot.igraph(year.g[[i]], layout = layout.circle, edge.arrow.size = .5, vertex.label = NA,
vertex.size = 5)
text(0, 0, label = levels(s.ocean2$year)[i], cex = 2)
}
web.props2 <- data.frame()
for (i in 1:45){
gind <- GenInd(get.adjacency(year.g[[i]], sparse = F))
diam <- diameter(year.g[[i]])
avpath <- average.path.length(year.g[[i]])
cluster <- transitivity(year.g[[i]])
cannibals <- sum(diag(get.adjacency(year.g[[i]], sparse = F)))
degrees <- degree(year.g[[i]], mode = "all")
indegrees <- degree(year.g[[i]], mode = "in")
outdegrees <- degree(year.g[[i]], mode = "out")
numBas <- length(indegrees[which(indegrees == 0)])
numTop <- length(outdegrees[which(outdegrees == 0)])
basal <- (numBas/gind$N) * 100
top <- (numTop/gind$N) * 100
int <- ((gind$N - (numBas + numTop))/gind$N) * 100
web.props <- data.frame(Year = levels(s.ocean2$year)[i], N = gind$N, L = gind$Ltot,
LD = gind$LD, C = gind$C, D = diam,
AvgPath = avpath, ClCoef = cluster, Can = cannibals, Bas = basal,
Top = top, Int = int)
web.props2 <- rbind(web.props2, web.props)
}
print(web.props2) Year N L LD C D AvgPath ClCoef Can Bas Top
1 1961 8 11 1.3750 0.196429 1 1.000 0.0000000 0 25.000 75.00
2 1962 8 16 2.0000 0.285714 1 1.000 0.0000000 0 50.000 50.00
3 1965 11 28 2.5455 0.254545 1 1.000 0.0000000 0 36.364 63.64
4 1966 8 7 0.8750 0.125000 1 1.000 0.0000000 0 12.500 87.50
5 1968 46 88 1.9130 0.042512 2 1.093 0.0000000 0 36.957 58.70
6 1969 12 20 1.6667 0.151515 1 1.000 0.0000000 0 16.667 83.33
7 1970 26 24 0.9231 0.036923 1 1.000 0.0000000 0 7.692 92.31
8 1971 10 16 1.6000 0.177778 1 1.000 0.0000000 0 20.000 80.00
9 1973 9 9 1.0000 0.125000 1 1.000 0.0000000 0 33.333 66.67
10 1974 49 58 1.1837 0.024660 1 1.000 0.0000000 0 6.122 93.88
11 1975 70 83 1.1857 0.017184 1 1.000 0.0000000 0 4.286 95.71
12 1976 28 38 1.3571 0.050265 1 1.000 0.0000000 0 14.286 85.71
13 1977 31 34 1.0968 0.036559 1 1.000 0.0000000 0 16.129 83.87
14 1979 95 157 1.6526 0.017581 1 1.000 0.0000000 0 14.737 85.26
15 1980 90 299 3.3222 0.037328 2 1.010 0.2691166 4 14.444 81.11
16 1981 94 139 1.4787 0.015900 2 1.042 0.0115607 1 11.702 86.17
17 1982 208 433 2.0817 0.010057 2 1.207 0.0101225 1 12.981 82.69
18 1983 299 4257 14.2375 0.047777 3 1.420 0.3121464 13 31.104 60.54
19 1984 109 163 1.4954 0.013846 2 1.190 0.0085511 1 9.174 87.16
20 1985 125 207 1.6560 0.013355 2 1.205 0.0144695 1 14.400 82.40
21 1986 120 219 1.8250 0.015336 1 1.000 0.0000000 0 10.833 89.17
22 1987 104 202 1.9423 0.018857 2 1.151 0.0000000 0 8.654 90.38
23 1988 155 825 5.3226 0.034562 3 1.119 0.0086548 0 21.290 70.97
24 1989 53 65 1.2264 0.023585 2 1.133 0.0164835 0 11.321 84.91
25 1990 129 224 1.7364 0.013566 2 1.189 0.0024430 1 6.977 89.15
26 1991 145 185 1.2759 0.008860 3 1.464 0.0132890 2 9.655 85.52
27 1992 130 210 1.6154 0.012522 3 1.290 0.0186722 1 10.769 86.92
28 1993 205 1230 6.0000 0.029412 4 1.336 0.0006669 1 14.634 81.95
29 1994 215 878 4.0837 0.019083 3 1.421 0.0179806 0 9.767 86.98
30 1995 213 382 1.7934 0.008460 3 1.799 0.0149495 1 5.164 90.61
31 1996 189 530 2.8042 0.014916 4 1.656 0.1237898 5 12.698 80.95
32 1997 205 422 2.0585 0.010091 3 1.099 0.0032805 1 11.707 85.37
33 1998 181 298 1.6464 0.009147 3 1.107 0.0050220 0 9.392 88.95
34 1999 183 599 3.2732 0.017985 3 1.290 0.0505352 1 10.929 78.69
35 2000 222 464 2.0901 0.009457 2 1.241 0.0189959 1 6.306 92.34
36 2001 161 296 1.8385 0.011491 3 1.317 0.0184049 1 6.832 89.44
37 2002 135 209 1.5481 0.011553 3 1.256 0.0156018 1 5.926 91.85
38 2003 60 87 1.4500 0.024576 3 1.442 0.0403769 1 6.667 88.33
39 2004 121 312 2.5785 0.021488 3 1.539 0.0496710 2 9.917 80.99
40 2005 57 69 1.2105 0.021617 2 1.374 0.0299700 2 1.754 94.74
41 2006 183 269 1.4699 0.008077 3 1.708 0.0408666 3 3.279 93.44
42 2007 63 62 0.9841 0.015873 1 1.000 0.0000000 0 1.587 98.41
43 2008 82 93 1.1341 0.014002 1 1.000 0.0000000 0 7.317 92.68
44 2009 71 78 1.0986 0.015694 1 1.000 0.0000000 0 4.225 95.77
45 2010 3 2 0.6667 0.333333 1 1.000 0.0000000 0 33.333 66.67
Int
1 0.0000
2 0.0000
3 0.0000
4 0.0000
5 4.3478
6 0.0000
7 0.0000
8 0.0000
9 0.0000
10 0.0000
11 0.0000
12 0.0000
13 0.0000
14 0.0000
15 4.4444
16 2.1277
17 4.3269
18 8.3612
19 3.6697
20 3.2000
21 0.0000
22 0.9615
23 7.7419
24 3.7736
25 3.8760
26 4.8276
27 2.3077
28 3.4146
29 3.2558
30 4.2254
31 6.3492
32 2.9268
33 1.6575
34 10.3825
35 1.3514
36 3.7267
37 2.2222
38 5.0000
39 9.0909
40 3.5088
41 3.2787
42 0.0000
43 0.0000
44 0.0000
45 0.0000ggplot(web.props2) + geom_histogram(aes(x = N), binwidth = 10)
ggplot(web.props2) + geom_point(aes(x = N, y = C))
Variation: 1990-2000
wp2 <- web.props2[25:35,]
ytind <- lapply(year.g[25:35], get.adjacency, sparse = F)
ytind <- lapply(ytind, TrophInd)
dtind <- cbind(rep(wp2$Year, sapply(ytind, nrow)), rbindlist(ytind))
ggplot(dtind, aes(x = TL, y = ..density..)) + geom_histogram(binwidth = .5) + facet_wrap(~V1)